Burning Library

Burning Library is a location in Tyranny.
 * In the Disfavored path, it is unlocked by asking Graven Ashe to explore the Library during Making a Stand, after learning of Amelia's fate or selecting it as the next sieging destination.
 * In the Scarlet Chorus path, it can be selected as the first or second territory to be secured. The third territory is always the Stone Sea.
 * In the Rebel path, it is unlocked if you choose the Sages as your final set of allies.
 * The Anarchist path will eventually lead you here.

Note that if you do not specifically unlock the library during Act II, your investigation for A Trial of Archons will suffer as you won't be able to explore it.

Background
Previously known as the Vellum Citadel, the archive and ancestral home of the Sages is now the site of a volcanic crater. Eruptions of lava began during the conquest of the Tiers, after Kyros' forces failed to claim the library in the Overlord's name. Kyros cast an Edict of Fire to break the siege and rid the world of the forbidden knowledge stored there. The Citadel has been a smoldering ruin ever since.

Just before the Young Fatebinder travels to Vendrien's Well to proclaim Kyros's Edict, the Scarlet Chorus took control of the Library.

Entrance

 * Welcome to the Library; hope you brought burn ointment. Find Foul Murmur torturing Folant to the northwest. Picking a fight with him means turning the whole camp hostile.
 * To the north of Foul Murmur and Folant is a plateau, which can be accessed from the upper ruins if you gave the Sages warning before casting the Edict of Fire during Conquest. Interact with the cross formations to gain the Sigil of Frostfire and +5 to Control Fire. A hidden container has the Emberglow Hood.
 * In the center is the Chorus camp around the entrance. The containers have minor loot, while the area near the entrance to the upper ruins has The Censor and Jelena (she only appears in the Disfavored path).

Upper ruins

 * Welcome to the finest place of higher learning in the Tiers! Excuse the dust. Lantry will remark on the forcefields when you enter, indicating that you need a specific sequence to unlock them. Further along he will point to the lake of lava, noting that it was where the Sages made parchment, down to the vats of rendering fat.
 * Further along you'll find a Sage feigning death (sarcastically remarking that they're so obviously dead earns favor with Bleden Mark). Asking to bind his wounds earns the opposite. He will point you to the pass-phrase, or rather, the first part of it. Pick the incomplete passphrase from the shelves (42 Lore required).
 * Use the nearby pile of rubble to grab the ink-stirring pole. Return to the first barrier and dispel it (interact with it once it changes to the sigil symbol).
 * Fat Ulsten lurks around the corner. Further still is Gaptooth. To the northwest is an exit onto the plateau with the magic cross formations (only available if you warned the Sages in advance). The Emberglow Hood is there. By touching the magic cross formations, you can learn the Sigil of Fire.
 * You can enter the Scriptorium with 44 Athletics. The Sage here carried a potion recipe for research at the Library Spire.
 * Beyond Gaptooth's little abode is a rope and pulley that allows you to slide down to the lower levels.

Lower ruins

 * Say hi to Numbly (or Gaptooth, if you had her slaughter Numbly with Subterfuge). Go upstairs near the statue to pilfer the Mindstatic Torc. Further to the northeast are more shelves, including another portion of the incomplete passphrase and The First Kings of Stalwart, which unlocks information necessary to end the Edict of Storms in Blade Grave without killing Amelia's daughter.
 * Rip out the Blood Chanter's Spine from the corpse of the Blood Chanter by the stairs. Yeah.
 * Continue south-west. Mind the trap. Loot the Research: Magic Sigil book from the shelves. You can divert to the island with the Scourges by jumping the lava gap with Athletics 49 and get some scrolls for your trouble.
 * Over the small bridge of lava is another section of the Library. If you want to save the two Maric Oath Bound, spring to the south-west and attack the beastwoman, preferably taunting her and her support to divert their attention away from the scout.
 * Defeat the nearby Bane and pick up the third part of the passcode. Head up the collapsed floor to the upper ruins.

Upper ruins revisited

 * Head east and meet Bone Whittler. Kill him. Grab the Sigil of Cyclical Energies from the shelves behind him.
 * Climb over the rubble piles (42 Athletics) to reach a Sage and an Oath Bound. Oh and the final part of the passcode. Watch Lantry flip out over the prospect of seeing the Silent Archive, then take a swig of one of his inks.
 * The Oath Bound will unlock the deserted battleground if you were at the Vellum Citadel during the Conquest and sent the Scarlet Chorus to find the lost Oath Bound patrol.
 * Rescuing the Sage and Oath Bound will net you 500 rings.
 * Use the pulley to the northwest to descend to the entrance to the Silent Archive storage area.

Lower ruins revisited

 * You arrive near the ward protecting the entrance to the Silent Archive. Wipe out the Bane to the south-west. Head to the barrier and kill whichever gang boss you left alive. Activate the runes as per the completed passphrase: ↑ ↓ ← → (Sigils of Vigor, Fire, Force, Stone).
 * The room by the barrier has the Sigil of Influential Domain on the shelves. The room with the staircase has Research: Shield Plans and a Sigil of Timeless Form (II). Descend down the staircase.

The Silent Archive

 * Head down the corridors to find the Silent Archive.... And the Censor. Kill her if you're not on the Chorus path.
 * Before you approach the Archive, explore the ledge around the lake to find an obsidian fragment, the Chronicler's Eye in a hidden compartment, the Staff of Hours, and the Elixir of Wits. Jackpot!

Post Edict of Fire

 * On non-Disfavored paths, you have the option of swapping an artifact for the Silent Archive, after reading the two sets of notes found around the Archive. Doing so ensures that the Library remains standing after the Edict of Fire ends. After the Edict ends, an area previously flooded with lava will now be available, but it's guarded by some Magebane.... and a Havoc.
 * On the Disfavored path, you'll not be able to save the Library. In fact, you can complete the destruction of knowledge by dropping the Silent Archive into lava.

Entrance

 * Foul Murmur and Folant: Found to the northwest.
 * The Censor: By the entrance.
 * Jelena: Bound to a post near the Censor. Does not appear in non-Disfavored paths.
 * Boltok: On a small island to the south-east.
 * After claiming the area for the Disfavored
 * Maric and Jelena (if she was released)
 * Lupin

Upper ruins

 * Fat Ulsten and Gaptooth
 * Bone Whittler

Lower ruins

 * Numbly

Loot

 * Emberglow Hood, Sigil of Fire: On the plateau with the cross formations, only accessible if you gave the Sages warning before casting the edict.
 * Mindstatic Torc: Lower ruins, in a hidden cache near the Sage statue.
 * The First Kings of Stalwart: On the shelves north of the Sage statue.
 * Blood Chanter's Spine: On the body of the Blood Chanter by the stairs near the statue.
 * Unraveler's Cane: In a hidden rubble pile in the south-east corner, opposite Bone Whittler.
 * Obsidian fragment, the Chronicler's Eye in a hidden compartment, the Staff of Hours, and the Elixir of Wits: On the ledge near the Silent Archive.
 * Hammer of Sunder: Located in the SW corner of the Burning Library. Area only accessible after the Edict of Fire is broken and the lava recedes. Naturally, this requires you to not destroy the library; it is thus inaccessible in a Disfavored run.
 * Banner of Ardent